Constraints of mixing angles from neutrino oscillation experiments and neutrinoless double beta decay

From the analyses of the recent data of neutrino oscillation experiments (especially the CHOOZ and the Super KAMIOKANDE experiments), we discuss how these data affect the neutrinoless double beta decay ($(\beta \beta {)}_{0\nu }$) rate and vice versa assuming that neutrinos are Majorana particles. For the case that $m_1\sim m_2\ll m_3$ ($m_i$ are neutrino masses), we obtain, from the data of the CHOOZ and Super KAMIOKANDE, $0.28 \le \sin^2\theta_{23} \le 0.76$and$\sin^2\theta_{13} \le 0.05$. Combining the latter constraint with the analysis of the “averaged” neutrino mass (< m_\nu >) appeared in $(\beta \beta){0\nu}$, we find that (\frac{< m\nu >-m_2}{m_3-m_2}<\sin^2 \theta_{13} \le 0.05), which leads to the constraint on (< m_\nu >) as (< m_\nu > \le 0.05 m_3+(1-0.05)m_2). For the case that $m_1\ll m_2\sim m_3$, we find that the data of neutrino oscillation experiments and$(\beta \beta {)}_{0\nu }$ imply the constraints of mixing angles.